In recent years various kinds of high speed digital wireless systems, such as mobile telephony, wireless LAN, Bluetooth, digital terrestrial television and the like, are being realized. Moreover, among digital semiconductor integrated circuits, analog technology similar to wireless circuitry is used in those that operate at high speeds of a GHz and above. In these circuits, an on-chip inductor formed on a semiconductor substrate is used as a passive device. The on-chip inductor is formed from metal wiring wound in a spiral shape in a semiconductor.
The on-chip inductor is much used as a part of a resonant circuit in an analog circuit. By connecting an inductor and a capacitor in series or in parallel to cause resonance, with a resonant frequency f0 determined by an inductance L of the inductor and a capacitance C of the capacitor, the resonance frequency being given by:
                              f          0                =                  1                      2            ⁢            π            ⁢                          LC                                                          (        1        )            the resonant circuit exhibits effects of high gain, impedance matching, oscillation, and the like. However, since resonance only occurs at frequencies in a narrow band close to the resonant frequency, in order to make a resonant circuit that operates at a variety of frequencies, it is necessary to change the resonant frequency. To change the resonant frequency f0, the inductance L or the capacitance C must be changed.
FIG. 20 is a circuit diagram of an amplifier that uses a resonant circuit. Referring to FIG. 20, a load formed of an inductor Ls and a capacitor Cs is connected to a MISFET M0. With transconductance of the MISFET M0 as Gm, and series resistance of the inductor Ls as Rs, if the series resistance of the capacitor Cs and parasitic capacitance outside of the capacitor Cs are ignored, gain G of the amplifier is:
                    G        =                              Gm            ×                          (                                                1                                                            ω                      2                                        ⁢                                          Cs                      2                                        ⁢                    Rs                                                  +                                  j                  ⁢                                      1                                          ω                      ⁢                                                                                          ⁢                      CsRs                                                                                  )                                =                      Gm            ×                          (                                                                                          ω                      2                                        ⁢                                          Ls                      2                                                        Rs                                +                                  j                  ⁢                                                            ω                      ⁢                                                                                          ⁢                      Ls                                        Rs                                                              )                                                          (        2        )            Here, the following holds:
  ω  =      1          LsCs      As long as there is no particular limitation, the inductance of the inductor is represented by a reference symbol the same as the inductor; the capacitance of the capacitor is represented by a reference symbol the same as the capacitor; and the resistance of a resistive element is represented by a reference symbol the same as the resistive element.
From Equation (2), the gain G of the amplifier decreases when the capacitance Cs is increased, and increases when the inductance Ls is increased. From Expression (1), in a case where the resonant frequency is changed by fixing the inductance Ls and changing the capacitance Cs, the gain G decreases on a low frequency side in which the capacitance Cs increases. Conversely, in a case where the capacitance Cs is fixed and the inductance Ls is changed, if the inductance Ls is increased, the gain G can be increased on the low frequency side.
In general, a method of changing the capacitance Cs is used in changing the resonant frequency ω. By a device such as a varactor using a p-n junction, a variable capacitor can be easily implemented on-chip. By Equation (2), it is desirable, with regard to a circuit characteristic, to change the inductance Ls, but with a conventional variable inductor, when the inductance Ls is changed, the series resistance Rs of the inductor Ls increases.
Next, a description is given concerning conventional variable inductance. FIG. 21 shows an equivalent circuit of a conventional magnetic field based variable inductor. On the other hand, FIG. 22 shows an equivalent circuit of a conventional switch based variable inductor.
Referring to FIG. 21, the magnetic field based variable inductor has a transformer formed of inductors LM1 and LM2. By connecting an n-type MISFET M1 to the inductor LM2 side, and changing an ON resistance, it is possible to change the inductance viewed from the two sides of the inductor LM1. Here, self-inductances of the inductors LM1 and LM2 are LM1 and LM2 respectively; mutual inductance of the inductor LM1 and the inductor LM2 is M; ON resistance of the MISFET M1 is R30; and series resistances of the inductances LM1 and LM2 are RM1 and RM2 respectively.
In this case, the inductance and the series resistance viewed from the two ends on the inductance LM1 side, in a case where the MISFET M1 is OFF, are as follows:Inductance LM1Resistance RM1  (3)
On the other hand, in a case where the MISFET M1 is ON,
                                          Inductance            ⁢                                                  ⁢            …            ⁢                                                  ⁢            LM            ⁢                                                  ⁢            1                    -                                    (                                                                    ω                    2                                    ⁢                                      k                    2                                    ⁢                  LM                  ⁢                                                                          ⁢                  1                  ⁢                  LM                  ⁢                                                                          ⁢                  2                                                                                            ω                      2                                        ⁢                    LM                    ⁢                                                                                  ⁢                                          2                      2                                                        +                                                            (                                                                        RM                          ⁢                                                                                                          ⁢                          2                                                +                                                  R                          ⁢                                                                                                          ⁢                          30                                                                    )                                        2                                                              )                        ⁢            LM            ⁢                                                  ⁢            2                          ⁢                                  ⁢                              Resistance            ⁢                                                  ⁢            …            ⁢                                                  ⁢            RM            ⁢                                                  ⁢            1                    +                                    (                                                                    ω                    2                                    ⁢                                      k                    2                                    ⁢                  LM                  ⁢                                                                          ⁢                  1                  ⁢                  LM                  ⁢                                                                          ⁢                  2                                                                                            ω                      2                                        ⁢                    LM                    ⁢                                                                                  ⁢                                          2                      2                                                        +                                                            (                                                                        RM                          ⁢                                                                                                          ⁢                          2                                                +                                                  R                          ⁢                                                                                                          ⁢                          30                                                                    )                                        2                                                              )                        ⁢            RM            ⁢                                                  ⁢            2                                              (        4        )            Here, a coupling coefficient k is
  k  =      M                  LM        ⁢                                  ⁢        1        ⁢        LM        ⁢                                  ⁢        2            
Referring to FIG. 22, the switch based variable inductor (for example, Patent Document 2) has two inductors LS1 and LS2, and these inductors are connected by an n-type MISFET M1 and a p-type MISFET M2. By turning only one of the MISFETs M1 and M2 ON by a control signal added to a control terminal CNT, it is possible to have the inductance viewed from the two sides as LS1 or LL1+LS2. An inductance that the switch based inductor can have is only the two values LS1 or LS1+LS2, and it is not possible to change the inductance analogically so as to have an intermediate value therebetween. However, in the switch based inductor it is possible to greatly change the inductance, in comparison to the magnetic field based inductor.
[Patent Document 1]
JP Patent Kokai Publication No. JP2007-005498A
[Patent Document 2]
JP Patent Kokai Publication No. JP-H07-142258A
[Patent Document 3]
JP Patent Kokai Publication No. JP-H08-045744A